Class TDistribution.StudentsTDistribution

java.lang.Object
org.apache.commons.statistics.distribution.AbstractContinuousDistribution
org.apache.commons.statistics.distribution.TDistribution
org.apache.commons.statistics.distribution.TDistribution.StudentsTDistribution
All Implemented Interfaces:
ContinuousDistribution
Enclosing class:
TDistribution
private static class TDistribution.StudentsTDistribution extends TDistribution
Implementation of Student's T-distribution.

  • Field Details

    • TWO

      private static final double TWO
      2.
      See Also:

    • CLOSE_TO_ZERO

      private static final double CLOSE_TO_ZERO
      The threshold for the density function where the power function base minus 1 is close to zero.
      See Also:

    • mvp1Over2

      private final double mvp1Over2
      -(v + 1) / 2, where v = degrees of freedom.

    • densityNormalisation

      private final double densityNormalisation
      Density normalisation factor, sqrt(v) * beta(1/2, v/2), where v = degrees of freedom.

    • logDensityNormalisation

      private final double logDensityNormalisation
      Log density normalisation term, 0.5 * log(v) + log(beta(1/2, v/2)), where v = degrees of freedom.

    • mean

      private final double mean
      Cached value for inverse probability function.

    • variance

      private final double variance
      Cached value for inverse probability function.

  • Constructor Details

    • StudentsTDistribution

      StudentsTDistribution(double degreesOfFreedom, double variance)
      Parameters:
      degreesOfFreedom - Degrees of freedom.
      variance - Precomputed variance

  • Method Details

    • computeVariance

      static double computeVariance(double degreesOfFreedom)
      Parameters:
      degreesOfFreedom - Degrees of freedom.
      Returns:
      the variance

    • density

      public double density(double x)
      Description copied from interface: ContinuousDistribution
      Returns the probability density function (PDF) of this distribution evaluated at the specified point x. In general, the PDF is the derivative of the CDF. If the derivative does not exist at x, then an appropriate replacement should be returned, e.g. Double.POSITIVE_INFINITY, Double.NaN, or the limit inferior or limit superior of the difference quotient.
      Parameters:
      x - Point at which the PDF is evaluated.
      Returns:
      the value of the probability density function at x.

    • logDensity

      public double logDensity(double x)
      Description copied from interface: ContinuousDistribution
      Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x.
      Parameters:
      x - Point at which the PDF is evaluated.
      Returns:
      the logarithm of the value of the probability density function at x.

    • cumulativeProbability

      public double cumulativeProbability(double x)
      Description copied from interface: ContinuousDistribution
      For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x). In other words, this method represents the (cumulative) distribution function (CDF) for this distribution.
      Parameters:
      x - Point at which the CDF is evaluated.
      Returns:
      the probability that a random variable with this distribution takes a value less than or equal to x.

    • getMean

      public double getMean()
      Description copied from class: TDistribution
      Gets the mean of this distribution.

      For degrees of freedom parameter \( v \), the mean is:

      \[ \mathbb{E}[X] = \begin{cases} 0 & \text{for } v \gt 1 \\ \text{undefined} & \text{otherwise} \end{cases} \]

      Specified by:
      getMean in interface ContinuousDistribution
      Specified by:
      getMean in class TDistribution
      Returns:
      the mean, or NaN if it is not defined.

    • getVariance

      public double getVariance()
      Description copied from class: TDistribution
      Gets the variance of this distribution.

      For degrees of freedom parameter \( v \), the variance is:

      \[ \operatorname{var}[X] = \begin{cases} \frac{v}{v - 2} & \text{for } v \gt 2 \\ \infty & \text{for } 1 \lt v \le 2 \\ \text{undefined} & \text{otherwise} \end{cases} \]

      Specified by:
      getVariance in interface ContinuousDistribution
      Specified by:
      getVariance in class TDistribution
      Returns:
      the variance, or NaN if it is not defined.

    • getMedian

      double getMedian()
      Description copied from class: AbstractContinuousDistribution
      Gets the median. This is used to determine if the arguments to the AbstractContinuousDistribution.probability(double, double) function are in the upper or lower domain.

      The default implementation calls AbstractContinuousDistribution.inverseCumulativeProbability(double) with a value of 0.5.

      Overrides:
      getMedian in class AbstractContinuousDistribution
      Returns:
      the median

    • createSampler

      public ContinuousDistribution.Sampler createSampler(org.apache.commons.rng.UniformRandomProvider rng)
      Description copied from class: AbstractContinuousDistribution
      Creates a sampler.
      Specified by:
      createSampler in interface ContinuousDistribution
      Overrides:
      createSampler in class AbstractContinuousDistribution
      Parameters:
      rng - Generator of uniformly distributed numbers.
      Returns:
      a sampler that produces random numbers according this distribution.